Geostatistical analysis and mapping for the year 2002 water levels in the High Plains aquifer of Kansas

by
Ricardo A. Olea and John C. Davis

Kansas Geological Survey

Report to the Director of the
Kansas Geological Survey
University of Kansas
Open-file Report No. 2002-14
Released April 2002, Electronic version created June 2002

Summary

Sixty-six wells placed into the network of observation wells in the last 3 years have had a beneficial effect either by replacing old observation wells that had mechanical problems or by increasing the sensitivity of the network to fluctuations in water depth. We have now provided an update to the network configuration that requires reactivation of 21 observation wells that were not measured this season and the addition of wells at 13 other key sites in the network.

The network detected an average water-table decline of 2.6 ft during the last 5 years, with some wells showing declines in excess of 30 ft, and a reduction in the number of areas where the water table is rising. In 2001, the 5-year decline was 1.7 ft. The decline is most severe in Groundwater Management District 3 in the southwest corner of the state, where depletion has changed the nature of the variation in the water table. During the period 1997-2002, the groundwater level in GMD3 has declined an average of 4.1 ft.

Table of Contents

• 1. Introduction
• 2. Year 2002 observation network
• 3. Water-table semivariogram modeling
• 4. Crossvalidation of year 2002 measurements
• 5. Water-table elevation in the High Plains aquifer
• 6. Kriging standard deviation map for water table
• 7. Water-table fluctuations in the last 5 years
• 8. Water-table fluctuations in the last year
• 9. Network analysis
• 10. Subdivision of the aquifer into homogeneous portions
• 11. Conclusions and recommendations
• References
• Appendix A. High Plains aquifer observation wells (available on "Data" section of CD-ROM website)

List of Figures

• 1. Histogram of water-table elevations
• 2. Semivariogram of water-table elevations
• 3. Crossvalidation estimates for water-table elevations
• 4. Normal confidence intervals
• 5. Cumulative distribution of depth to water in the last 5 years
• 6. Semivariogram of depth to water in the last 5 years
• 7. Crossvalidation results for 5-year fluctuations in water table
• 8. Cumulative distribution of depth to water during the last year
• 9. Semivariogram of depth to water during the last year
• 10. Summary of crossvalidation results for fluctuation in water-table elevation during 2001
• 11. Hexagonal pattern used to graphically locate sites in need of new wells
• 12. Semivariogram models along the trend-free direction for each groundwater management district and for the entire aquifer

List of Tables

• 1. Classification of year 2002 observation wells
• 2. Observation wells that should be measured next year
• 3. Wells excluded from data extraction that should be reactivated
• 4. Ideal locations for new observation wells
• 5. Parameters for the semivariograms in Figure 10

List of Plates The 2002 maps are presented as Adobe Acrobat PDF files. You will need the Acrobat PDF Reader, available free from Adobe, to read the maps.

1. Measured observation wells in the High Plains aquifer, Dec. 2001-Feb. 2002 (243 k)
2. High Plains aquifer observation wells not measured, Dec. 2001-Feb. 2002 (112 k)
3. Water-table elevation of the High Plains aquifer, Dec. 2001-Feb. 2002 (231 k)
4. Kriging standard deviation, Dec. 2001-Feb. 2002 (583 k)
5. Change in depth to water over the last 5 years (517 k)
6. Kriging standard deviation for 5-year fluctuations (788 k)
7. Change in depth to water over the last year (328 k)
8. Kriging standard deviation for last year fluctuations (832 k)
9. Kriging standard deviation employing all observation wells (563 k)
10. Kriging standard deviation after proposed network enhancement (543 k)
11. Kriging standard deviation for GMD1 (144 k)
12. Kriging standard deviation for GMD2 (148 k)
13. Kriging standard deviation for GMD3 (183 k)
14. Kriging standard deviation for GMD4 (206 k)
15. Kriging standard deviation for GMD5 (161 k)
16. Water-table elevation of the High Plains aquifer in GMD4 (138 k)
17. Water-table elevation of the High Plains aquifer in GMD3 (141 k)

The objective of this report is to analyze and map fluctuations in depth to water in the High Plains aquifer for the purpose of:

• Detecting fluctuations in the water-table elevation;
• Detecting inaccuracies in the measurement process and suggesting ways to improve field procedures and archiving;
• Determining where the observation-well network can be improved for greater efficiency and reliability.

For year 2002, the extraction includes wells measured during the period December 1, 2001, through February 28, 2002. For convenience we refer to this period as the "2002 season." The same 3-month span was used to extract measurements made in 1996-1997 and in 2000-2001. For wells having more than one measurement during a 3-month interval, the shallowest reading was used.

There are 122 observation wells that monitor aquifers other than the High Plains aquifer, leaving for this study the 1239 wells listed in Appendix A. Two wells, no. 762 (22S 15W 03AAA 01) and no. 763 (22S 15W 03AAA 02), are so close together that they have the same state plane coordinates, which results in identical UTM coordinates if these are calculated from the legal description rather than measured in the field with a GPS device. Thus well no. 763 was not included in this analysis because the geostatistical techniques employed do not allow multiple measurements at the same location. Consequently, the number of wells used in this study is 1238, an increase of four wells over the number used a year ago (Olea and Davis, 2001).

The observation wells used in the study are summarized in Table 1 and posted on Plates 1 and 2. "Provisional wells" are those which have been measured only since 1999. These wells become official observation wells if they can be measured consistently for 3 years and yield systematic readings. Note that the wells are labeled on the maps with arbitrary sequential numbers rather than the longer U.S. Geological Survey (USGS) or KGS official well designations. The water-table elevations measured in 1173 wells are summarized in graphic form in Figure 1.

	Network		Provisional		Total
	Measured	Not measured	Measured	Not measured
KGS	410	10	36	3	459
DWR	705	47	22	5	779
Total	1115	57	58	8	1238

Figure 1. Histogram of water-table elevations in the High Plains aquifer of Kansas, December 2001-February 2002.

Figure 2. Semivariogram of the 2002 water-table elevation along N10E, the trend-free direction of the Kansas High Plains aquifer. Dots indicate estimated values. The solid line is the best-fitting permissible model, which is Gaussian with a nugget value of 68 ft², a value of 10645 ft² for the sill minus the nugget, and a range of 63.5 km.

The most anomalous wells are no. 254 (28S 42W 20BCC 01) and no. 905 (17S 42W 28DAB 01). Inspection of the measurements and the locations of these wells does not suggest anything improper in the data collection or recording.

5. Water-table Elevation in the High Plains Aquifer

The water-table surface does not appear to differ much from the surfaces observed in previous years (Miller, Davis, and Olea, 1998; Olea and Davis, 1999a; Olea and Davis, 2000a; Olea and Davis, 2001). This year-to-year similarity is partly the reason for mapping annual differences in water level, as the difference maps reveal more subtle variations than do the maps of elevation themselves.

6. Kriging Standard Deviation for Water Table

The distribution of the differences between observations and estimations seen in crossvalidation indicates that it is reasonable in this instance to assume that the kriging estimation errors are normally distributed. With this assumption, Figure 4 can be used to estimate confidence intervals about the kriged surface.

For example, if at a specific location the kriging estimate is 3000 ft and the kriging standard deviation is 10 ft, then the probability is 90% that the true water level elevation lies between 2983.5 and 3016.5 ft and the probability is 99% that the true elevation is between 2974.2 and 3025.8 ft.

Figure 4. Standard normal score versus probability. Given any kriging estimate and a value of the standard normal score a, the ordinate gives the probability that the true value is within an interval given by (the estimated value minus a times the kriging standard deviation) and (the estimated value plus a times the kriging standard deviation).

Figure 5. Cumulative probability distribution of differences in depth to water during the last 5 years in the High Plains aquifer.

Figure 6. Experimental semivariogram of differences in depth to water over the 5-year period 2002-1997 in 1085 observation wells in the High Plains aquifer. Line is the best-fit model, which is exponential with a nugget of 0.3 ft², range of 27.7 km, and a value of 23.5 ft² for the sill minus the nugget.

Figure 7. Crossvalidation estimates for changes in water-table elevation over the 5-year period from 1997 to 2002.

General trends in the mapped surface are similar to those observed on previously computed maps of changes in water level over 5-year periods (Miller, Davis, and Olea, 1998; Olea and Davis, 1999a; Olea and Davis, 2000a; Olea and Davis, 2001). However, the rate of depletion seems to be worsening at an accelerated pace. The average increase in depth to the water table in an observation well is 2.6 ft over the period 1997-2002, which is greater than the 1.7 ft average increase in depth seen during the previous 5-year period (1996-2001) or the 1.1 ft average increase in depth for 1995-2000.

Plate 6 shows the kriging standard deviation of the estimated 5-year change shown in Plate 5. Use of these maps in combination with Figure 4 indicates that all areas where depletion is greater than 5 ft (i.e., all areas below the -5 ft contour line) are real and cannot be dismissed as artifacts of the contouring procedure. This also is true for the much smaller areas of recharge where the increase in water level is greater than 5 ft.

8. Changes in the Water Table Over the Past Year

Figure 8. Cumulative probability distribution of the change in depth to water during the last year, 2001-2002.

Figure 9. Experimental semivariogram of differences in depth to water in 1143 observation wells in the High Plains aquifer for the period 2001-2002. Line is the best-fit model, which is exponential with a nugget of 0.3 ft², range of 20.4 km, and value of 4.4 ft²for the sill minus the nugget.

The Kansas Geological Survey and the Division of Water Resources have agreed that the observation-well network should be arranged in such a way that the kriging standard deviation is less than 10 ft everywhere within the High Plains aquifer except near the aquifer boundaries. This section updates recommendations made in past years whose intent was to completely eliminate areas within the network where the kriging standard deviation exceeds the agreed-upon limits (Olea, 1997a; Olea, 1997b; Olea and Davis, 1999b; Olea and Davis, 2000a; Olea and Davis, 2000b; Olea and Davis, 2001). Table 2 lists 17 of the 65 wells that were not measured this season; if these wells had been measured, all areas where uncertainty in the network exceeds acceptable limits would have been eliminated or significantly reduced.

Table 2. Observation wells that should be measured next year.

Seq. no.	USGS ID	KGS ID	Agency
91	371801101363101	32S 39W 06BBB 01	DWR
110	372128101065001	31S 35W 15BAA 01	KGS
131	372405100515601	30S 32W 31BAB 01	KGS
233	373412101180101	28S 36W 31BDD 01	KGS
347	374206101191201	27S 37W 13BD 01	DWR
388	374417100280401	26S 29W 35CCC 01	KGS
454	374926099071601	25S 16W 31DCC 01	DWR
468	375008099141501	25S 17W 31BBD 01	DWR
547	375521100363801	24S 30W 33ADD 01	KGS
554	375557100515801	24S 32W 30DDD 01	KGS
644	380106100434402	23S 31W 28CDD 02	KGS
669	380217098071401	23S 07W 20BCA 01	DWR
736	380801100554801	22S 33W 22BAA 01	KGS
769	381120098434802	21S 13W 27DDD 02	DWR
795	381504098465101	21S 13W 05CBD 01	DWR
969	384323101372101	15S 39W 26ACC 01	DWR
976	384644101420801	15S 39W 06CBC 01	DWR

Table 3 lists four observation wells that did not appear in the 2002 data extraction, apparently because these wells are no longer included in the network. These wells should be reactivated or replaced by nearby wells.

Table 3. Wells not included in the 2002 data extraction that should be reactivated.

Seq. no.	USGS ID	KGS ID	Agency
2001	372944100474902	29S 32W 26CBB 02	KGS
2002	372855100335801	29S 30W 35ACD 01	KGS
2003	372816100441901	30S 31W 05BBB 01	KGS
2615	375811097373001	24S 03W 14BBB 01	DWR

Finally, it is necessary to add 13 new observation wells at or near the locations listed in Table 4; this will completely eliminate areas inside the High Plains aquifer that have kriging standard deviations greater than 10 ft. These locations have been determined by placing hypothetical observation wells at the centers of the hexagons shown in Figure 11. The most efficient way of sampling a two-dimensional continuous variable is to take measurements at the centers of regular hexagons that form a tessellation of the area of interest. Based on past experience, there is some leeway in locating wells and they do not have to be at the center of a perfectly hexagonal network. Usually, if a replacement well is in the same section as the well it replaces, or in any of the contiguous sections, the replacement well will be almost as effective in reducing the kriging standard deviation. Plate 10 confirms that, under the proposed enhancements, the kriging standard deviation is less than 10 ft at all locations except adjacent to the boundaries of the aquifer.

Table 4. Ideal locations for new observation wells.

Seq. no.	UTM X (meters)	UTM Y (meters)	Legal location
3001	305000	4480000	4S 35W 5CCA
3002	312500	4397000	4S 35W 13DAA
3003	352000	4378000	6S 31W 12DDC
3004	335000	4355000	8S 32W 29ACD
3005	351000	4193000	25S 31W 14CDD
3006	350000	4183000	26S 31W 15CCA
3007	318000	4139000	31S 34W 6ACD
3008	319000	4130000	31S 34W 32CDD
3009	312000	4160000	34S 35W 3BDC
3010	343000	4130000	31S 32W 35CAD
3011	572000	4207000	23S 8W 34ADA
3012	348000	4347000	9S 31W 22AAC
3013	300000	4119000	33S 36W 8ABA

Figure 11. Hexagonal pattern used graphically to locate sites where new wells are needed.

Figure 12 and Table 5 show five semivariograms, one for each groundwater management district. Also shown for comparison is the aquifer-wide average semivariogram from Figure 2.

Figure 12. Semivariogram models along the trend-free direction for each groundwater management district and for the entire aquifer. Table 5 lists values of the critical parameters.

Table 5. Parameters for the semivariogram models in Figure 11. All models are Gaussian.

Area	Measurements	No trend (degree)	Nugget (sq ft)	Sill (sq ft)	Range (km)	AIC
GMD1	126	N8E	60	1118	21.894	-33.9
GMD2	103	N2W	43	1587	50.916	-30.8
GMD3	378	NS	272	12774	74.290	-100.0
GMD4	339	N22W	77	2695	35.766	-26.8
GMD5	227	N10W	69	2105	52.592	-73.5
Entire aquifer	1173	N10E	68	10713	63.528	-109.2

Although the semivariograms of the other districts have sills that are significantly different than that of the semivariogram for the entire aquifer, the kriging standard deviation maps of the districts show minimal differences, especially that of GMD5. The kriging standard deviations for GMD2 are approximately 20% lower than standard deviations calculated across the entire aquifer; those for GMD1 and GMD4 are about 20% higher.

Because the spatial continuity of the water-level elevation differs from district to district, the network density should also differ in order to maintain uniform reliability. However, the High Plains aquifer observation-well network is designed as a constant-density network. Reducing the average kriging standard deviation by half within an area would require that the number of wells be increased 16 fold (Olea, 1984). The obvious impracticality of such a step means we will have to live with varying network reliability, which may even become more severe if groundwater depletion continues to worsen.

Except in GMD3, using semivariogram models by district rather than statewide does not significantly change the contour maps of water-table elevation, as can be seen by comparing Plates 3 and 16. Increase in the nugget has the effect of increasing the smoothing in the kriging estimates, observable in Plate 17.

11. Conclusions and Recommendations

• Depletion of the aquifer continued at an accelerated average pace of a 2.6-ft drop in water level in the last 5 years, an increase from the drop of 1.7 ft for the period 1996-2001;
• Based on calculations using a single semivariogram for the entire aquifer, to limit the kriging standard deviation to 10 ft except near the aquifer boundary, four wells that were not measured this year must be returned to the network, 17 provisional wells that were not measured during the 2002 season must be included, and 13 additional wells must be added to the network;
• Subdividing the aquifer into groundwater management districts for geostatistical analysis results in kriging standard deviations for GMD3 that are approximately twice as high as those predicted using one semivariogram for the entire aquifer. This reflects heterogeneity that is probably due to severe depletion of the aquifer in this area. At this time, no special additions to the observation network are proposed to counteract this problem.
• Wells no. 254 (28S 42W 20BCC 01) and no. 905 (17S 42W 28DAB 01) have abnormal water levels in 2002. Well no. 965 (15S 42W 32BDA 01) is also exhibits aberrant behavior for the 5-year period 1997- 2002, as do wells no. 159 (30S 40W 12BBB 01), no. 875 (18S 38W 23BAB 01), and no. 760 (22S 17W 05BBC 02). Well no. 760 shows an abnormal 1-year fluctuation, as do wells no. 320(27S 23W 28AAA 01) and no. 1054 (07S 27W 22DAC 01). A special review and evaluation of these anomalous wells are recommended.

Olea, R.A., 1984, Sampling design optimization for spatial functions: Mathematical Geology, vol. 16, no. 4, p. 369-392.

Olea, R.A., 1997a, Sampling analysis of the annual observation water-level wells in Kansas: Kansas Geological Survey Open-File Report No. 97-73, 44 p.

Olea, R.A, 1997b, Modification to the High Plains aquifer observation network expansion in Open-File Report No. 97-73: Open-file Report 97-84, Kansas Geological Survey, Lawrence, Kansas, 3 p.

Olea, R.A., 1999, Geostatistics for Engineers and Earth Scientists: Kluwer Academic Publishers, Norwell, Massachusetts, 303 p.

Olea, R.A., and J.C. Davis, 1999a, Sampling analysis and mapping of water levels in the High Plains aquifer of Kansas: Kansas Geological Survey Open-File Report No. 99-11, 35 p., 9 plates.

Olea, R.A., and J.C. Davis, 1999b, Optimization of the High Plains aquifer water-level observation network: Kansas Geological Survey Open-File Report No. 99-15, 8 p., 3 plates.

Olea, R.A., and J.C. Davis, 2000a, Year 2000 sampling analysis and mapping of water levels in the High Plains aquifer of Kansas: Kansas Geological Survey Open-File Report No. 2000-13, 33 p., 5 plates.

Olea, R.A., and J.C. Davis, 2000b, Year 2000 proposed additions to the High Plains aquifer water-level observation network: Kansas Geological Survey Open-File Report No. 2000-17, 7 p., 1 plate.

Olea, R.A., and J.C. Davis, 2001, Year 2001 mapping of water levels in the High Plains aquifer of Kansas and analysis of the monitoring network: Kansas Geological Survey Open-File Report No. 2001-6, 49 p., 8 plates. [Maps Available Online]

Appendix A--High Plains aquifer observation wells